Chapter 2: Organizing the Data PDF

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e Chapter 2: Organizing the Data © 2014 by Pearson Higher Education, Inc 1 Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use...

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e Chapter 2: Organizing the Data © 2014 by Pearson Higher Education, Inc 1 Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use CHAPTER OBJECTIVES 2.1 Create frequency distributions of nominal data 2.2 Calculate proportions, percentages, ratios, and rates 2.3 Create simple and grouped frequency distributions 2.4 Create cross-tabulations 2.5 Distinguish between various forms of graphic presentations © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes Create frequency distributions of 2.1 nominal data Internal Use 2.1 Introduction Formulas and statistical techniques are used by researchers to: Organize raw data Test hypotheses Raw data is often difficult to synthesize Frequency tables make raw data easier to understand 4 Internal Use 2.1 Frequency Distributions of Nominal Data Characteristics of a frequency distribution of nominal data: Responses of Young Boys to Title Removal of Toy Consists of two columns: Response of Child f Left column: Cry 25 characteristics (e.g., Response of Child) Express Anger 15 Right column: frequency Withdraw 5 (f) Ply with another toy 5 N=50 5 Internal Use 2.1 Comparing Distributions Comparisons clarify results, add information, and allow for comparisons Response to Removal of Toy by Gender of Child Gender of Child Response of Child Male Female Cry 25 28 Express Anger 15 3 Withdraw 5 4 Play with another toy 5 15 Total 50 50 6 Internal Use Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes Calculate proportions, percentages, 2.2 ratios, and rates Internal Use 2.2 Proportions and Percentages Allows for a comparison of groups of different sizes Proportion – number of cases compared to the total size P= f of distribution N Percentage – the frequency of f occurrence of a category per % = (100) N 100 cases 8 Internal Use 2.2 Ratio and Rates Ratio – compares the frequency f1 of one category to another Ratio = f2 Rate – compares between  f actual cases  Rate = (1,000 )   actual and potential cases  f potential cases  9 Internal Use Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes Create simple and grouped 2.3 frequency distributions Internal Use 2.3 TABLE 2.4 The Distribution of Marital Status Shown Three Ways Marital Status f Marital Status f Marital Status f Married 30 Single 20 Previously married 10 Single 20 Previously married 10 Married 30 Previously married 10 Married 30 Single 20 Total 60 Total 60 Total 60 Table 2.4 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.3 TABLE 2.5 A Frequency Distribution of Attitudes toward a Proposed Tuition Hike on a College Campus: Incorrect and Correct Presentations Attitude toward Attitude toward a Tuition Hike f a Tuition Hike f Slightly favorable 2 Strongly favorable 0 Somewhat unfavorable 21 Somewhat favorable 1 Strongly favorable 0 Slightly favorable 2 Slightly unfavorable 4 Slightly unfavorable 4 Strongly unfavorable 10 Somewhat unfavorable 21 Somewhat favorable 1 Strongly unfavorable 10 Total 38 Total 38 INCORRECT CORRECT Table 2.5 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use Grouped Frequency Distribution of 2.3 Interval Data Used to clarify the presentation of interval-level scores spread over a wide range Class Intervals Smaller categories or groups containing more than one score Class interval size determined by the number of score values it contains 13 Internal Use TABLE 2.7 Grouped Frequency 2.3 Distribution of Final-Examination Grades for 71 Students Class Interval f % 95–99 3 4.23 90–94 2 2.82 85–89 4 5.63 80–84 7 9.86 75–79 12 16.90 70–74 17 23.94 65–69 12 16.90 60–64 5 7.04 55–59 5 7.04 50–54 4 5.63 Total 71 100 a a The percentages as they appear add to only 99.99%. We write the sum as 100% instead, because we know that.01% was lost in rounding. Table 2.7 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.3 Class Limits and the Midpoint Class Limits The point halfway between i =U −L adjacent intervals Upper and lower limits i = size of a class interval – Distance from upper and U = upper limit of a class interval lower limit determines the size of class interval L = lower limit of a class interval The Midpoint The middlemost score value in a class interval – The sum of the lowest and highest value in a class interval divided by two lowest score value + highest score value m= 2 15 Internal Use 2.3 Cumulative Distributions Cumulative Frequencies Total number of cases having a given score or a score that is lower – Shown as cf – Obtained by the sum of frequencies in that category plus all lower categories’ frequencies Cumulative Percentage Percentage of cases having a given score or a score that is lower cf c % = (100 ) N 16 Internal Use TABLE 2.7 Grouped Frequency 2.3 Distribution of Final-Examination Grades for 71 Students Class Interval f % 95–99 3 4.23 90–94 2 2.82 85–89 4 5.63 80–84 7 9.86 75–79 12 16.90 70–74 17 23.94 65–69 12 16.90 60–64 5 7.04 55–59 5 7.04 50–54 4 5.63 Total 71 100 a a The percentages as they appear add to only 99.99%. We write the sum as 100% instead, because we know that.01% was lost in rounding. Table 2.7 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.3 Percentiles The percentage of cases falling at or below a given score Deciles – points that divide a distribution into 10 equally sized portions Quartiles – points that divide a distribution into quarters Median – the point that divides a distribution in two, half above it and half below it 18 Internal Use Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 2.4 Create cross-tabulations Internal Use 2.4 Table 2.17 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.4 Percents within Cross-Tabulations f Total Percents: total % = (100 ) Ntotal f Row Percents: row % = (100 ) Nrow f Column Percents: column% = (100 ) Ncolumn The choice comes down to which is more relevant to the purpose of the analysis If the independent variable is on the rows, use row percents If the independent variable is on the columns, use column percents If the independent variable is unclear, use whichever percent is most meaningful 21 Internal Use 2.4 Table 2.18 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes Distinguish between various forms of 2.5 graphic presentations Internal Use 2.5 Figure 2.4 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.5 Figure 2.6 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.5 Figure 2.9 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.5 Figure 2.11 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.5 Figure 2.12 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.5 Figure 2.14 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved Internal Use 2.5 Figure 2.15 © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved  CHAPTER SUMMARY Internal Use Frequency distributions can be created to help researchers 2.1 visualize distributions Proportions, percentages, ratios, and rates can be calculated as 2.2 a way to describe data Simple frequency distributions can be created using data at any 2.3 level of measurement, while interval level data is needed to create a grouped frequency data Cross-tabulations can be created to illustrate the relationship 2.4 between two variables Several forms of graphs can be used to demonstrate patterns 2.5 and relationships between variables © 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey 07458 All Rights Reserved